Support overlapping $L_{1}$ contractions and exact non-singular transformations
Volume 84 / 2000
Colloquium Mathematicum 84 (2000), 515-520
DOI: 10.4064/cm-84/85-2-515-520
Abstract
Let T be a positive linear contraction of $L_{1}$ of a σ-finite measure space (X,Σ,μ) which overlaps supports. In general, T need not be completely mixing, but it is in the following cases: (i) T is the Frobenius-Perron operator of a non-singular transformation ϕ (in which case complete mixing is equivalent to exactness of ϕ). (ii) T is a Harris recurrent operator. (iii) T is a convolution operator on a compact group. (iv) T is a convolution operator on a LCA group.
